Singular Hessians

Determinant of Complexes and Higher Hessians

Abstract. Let X ⊂ Pr be a smooth algebraic curve in projective space, over an algebraically closed field of characteristic zero. For each m ∈ N, the m-flexes of X are defined as the points where the osculating hypersurface of degree m has higher contact than expected, and a hypersurface H ⊂ Pr is called a m-Hessian if it cuts X along its m-flexes. When X is a complete intersection, we give an e...

Gradients and Hessians in Hilbert spaces

Complexity of Gradients, Jacobians, and Hessians

Fast Approximation of Rotations and Hessians matrices

A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix Q with linearithmic complexity, i.e. with 1 2 n lg(n) rotations over pairs of coordinates, arranged in an FFT-like fashion. The approximation is “learned” using gradient descent. It allows to represent symmetric matrices H as QDQ where D is a diagonal matrix. It c...

On Variable - Metric Methods for Sparse Hessians

The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis's nonsparse symmetrization formula derived. A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed. The sparse BFGS generated by this method...